the product of 12 and K is 84 solve for K K =

The correct question is;

Joey borrows $2400 from his grandfather and pays the money back in monthly payments of $200.

a. Write a linear function that represents the remaining money owed L(x) after x months.

b. Evaluate L(10) and interpret the meaning in the context of this problem.

A) L(x) = 200x + 2400; L(10) = 4400, This represents the amount Joey still owes his

grandfather after 10 months.

B) L(x) = -200x + 2400; L(10) = 400, This represents the amount Joey has paid his

grandfather after 10 months.

C) L(x) = 200x + 2400; L(10) = 4400, This represents the amount Joey has paid his

grandfather after 10 months.

D) L(x) = -200x + 2400; L(10) = 400, This represents the amount Joey still owes his

grandfather after 10 months.

Answer:

A) L(x) = 2400 - 200x

B) Option D is correct

Step-by-step explanation:

A) We are told that Joey borrowed 2400.

Now he pays back in installments of 200 every month.

Thus for x number of months he would have paid 200x.

Thus,the linear function that represents the remaining money owed is;

L(x) = 2400 - 200x

B) L(10) = 2400 - (200 * 10)

L(10) = 2400 - 2000

L(10) = 400

Thus, after 10 months, Joey is owing 400.

So, looking at the given options, the correct one is option D.

Answer:

(-2, -(2pi)/3)

Step-by-step explanation:

a p ex

In da pic :)))))))))

Answer:

19/70 of NASA shuttle missions were carried out by Discovery.

9/140 of NASA shuttle missions were carried out by Challenger.

17/70 of NASA shuttle missions were carried out by Endeavour.

Step-by-step explanation:

Adding the number of missions carried out by NASA gives us 140 in total.

Discovery's total amount of missions simplified is 19/70.

Challenger's total amount of missions is already in the simplest form.

Endeavour's total amount of missions simplified is 17/70.

Answer:

81/140

Step-by-step explanation:

Well to find the fraction we first need to total amount of NASA missions.

38 + 32 = 70

70 + 34 = 104

104 + 27 = 131

131 + 9 = 140

Now we need to find out the amount of Discovery, Challenger, and Endeavour missions.

38 + 9 + 34 = 81

Now we can make the following fraction,

81/140

This is already in simplest form.

Thus,

the answer is 81/140.

Hope this helps :)

Answer:

ans1 9/11

ans2 8/52

it is because the reciprocol means the opposite of the the give value

Answer:

Step-by-step explanation:

a.

[tex] \frac{11}{9} [/tex]

Just flip the fraction, you will get:

[tex] \frac{9}{11} [/tex]

b.

[tex]5 \frac{1}{8} [/tex]

The first thing you have to do is that convert the mixed fraction into improper fraction.

To convert mixed fraction into improper fraction, you have to rewrite the denominator which is 8 , Thenafter you have to multiply 5 and 8 and then add 1

It would be:

[tex] \frac{5 \times 8 + 1}{8} [/tex]

[tex] = \frac{40 + 1}{8} [/tex]

[tex] = \frac{41}{8} [/tex]

Now , you have to flip it in order to get reciprocal:

[tex] = \frac{8}{41} [/tex]

Answer:

B

Step-by-step explanation:

Answer:

-2             7

-1             -6

Step-by-step explanation:

I used a calculator.

Answer:

21 feet 4 inches

Step-by-step explanation:

Ellie bought two planks of wood that were each 4ft 3in long

Total length of these two planks = 4ft 3in + 4ft 3in = 8 feet 6 inches

she also bought  two planks of wood that were each 6 ft 5in long

Total length of these two  6 ft 5in planks =  6 ft 5in +  6 ft 5in = 12 feet10 inches

Thus, total length of all the woods purchased = Total length of 4ft 3in two planks  + Total length of the two  6 ft 5in planks

= 8 feet 6 inches + 12 feet 10 inches

adding feet with feet and inches with inches term

= 20 feet 16 inches

we know that 12 inches is equal to 1 feet

thus, 16 inches can be written as 1 feet 4 inches

thus,

20 feet 16 inches will be same as 21 feet 4 inches

The total length of the wood Ellie purchased is 21 feet 4 inches.

Answer:

I dont give the answer right away so you read what i write and fully understand :D

Step-by-step explanation:

The reciprocal of something is basically when you flip something over. Since 17h/46j is a fraction, the reciprocal is 46j/17h. Remember, a number times the reciprocal is always equal to one.

Answer:

46j over 17h

Step-by-step explanation:

a reciprocal fraction is formed by flipping the fraction around

for example:

2/3

reciprocal= 3/2 or 1.5

HOPE THIS HELPS!!! :)

Here is the step by step answer. hope it helps!

The solution to the quadratic equation x² - 3x + 8 = 0 is given by

x = ( 3/2 ) ± i ( √23/2 )

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² - 3x = -8  

Adding 8 on both sides of the equation , we get

x² - 3x + 8 = 0   be equation (1)

Now , on simplifying the equation , we get

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

Substituting the values in the equation , we get

x = [ - ( -3 ) ± √ ( -3 )² - ( 4 ) ( 1 ) ( 8 ) ] / 2

On simplifying the equation , we get

x = [ 3 ± √ ( 9 - 32 ) ] / 2

x = ( 3/2 ) ± √ ( -23 ) / 2

x = ( 3/2 ) ± i ( √23/2 )

where i² = -1

Therefore , the value of x is  x = ( 3/2 ) + i ( √23/2 ) , x = ( 3/2 ) - i ( √23/2 )

Hence , the solution to the equation is x = ( 3/2 ) ± i ( √23/2 )

To learn more about quadratic equations click :

https://brainly.com/question/25652857

#SPJ2

Answer:

98.5

Step-by-step explanation:

The dude above do be wrong doh

Answer:

1. Average Number of Steps of

= Total of the different steps /  divided by 3

= 6,943/3

= 2,314.3 steps

2. Weighted Average Number of Steps of 3, 58-inch, 5, 64-inc, and 2, 76-inch people

= Total steps by the 10 people divided by 10

= 23,558/10

= 2,355.8 steps

3. The difference is not much.

4. The weighted average (2,355.8 steps) is a more accurate representation of the data.  The calculation of the ordinary average steps is more confusing than the weighted average steps.

Step-by-step explanation:

1. Calculation of the Weighted Average Number of Steps of:

3, 58-inch people = 3 x 2,601 =   7,803

5, 64-inch people = 5 x 2,357 = 11,785

2, 76-inch people = 2 x 1,985 =  3,970

10 persons' total steps = 23,558

2. Calculation of the ordinary average:

58-inch people =  2,601

64-inch people =  2,357

76-inch people =  1,985

Total steps           6,943

Hey there! I'm happy to help!

If we add Machine 1's 459 satisfactory pistons and 51 unsatisfactory pistons, we get 510 total pistons.

If we add Machine 2's 360 satisfactory pistons and 40 unsatisfactory pistons, we get 400 total pistons.

First, we want to find the probability of choosing an unsatisfactory piston from Machine 1.

We see that 51/510 (unsatisfactory pistons out of total pistons) simplifies to equal 1/10, so there is a 1/10 chance of getting an unsatisfactory piston from Machine 1.

For Machine 2, there are 360 satisfactory and 400 total. This gives us 360/400, which simplifies to 9/10.

Now, we multiply our two probabilities together to find the probability that they both happen.

1/10×9/10=9/100

Therefore, the probability that a piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory is 9/100 or 9%.

Have a wonderful day! :D

Hi there! :)

Answer:

w = 7 cm.

Step-by-step explanation:

Given:

P = 56

Use the formula P = 2l + 2w to solve for the perimeter of the rectangle.

Let w = width, and

3w = length

Plug these into the equation:

56 = 2(3w) + 2(w)

56 = 6w + 2w

Combine like terms:

56 = 8w

Divide both sides by 8:

w = 7 cm.

The width of rectangle is 7 cm.

Answer:

The  p-value is  [tex]p-value = 0.013167[/tex]

Step-by-step explanation:

From the question we are told that

     The  population mean is [tex]\mu[/tex] =  200 milligrams

     The sample size is [tex]n = 70[/tex]

     The sample  mean is  [tex]\= x = 205.7[/tex]

      The  sample standard deviation is  [tex]\sigma = 21 \ milligram[/tex]

Generally the Null hypothesis is  mathematically represented as

      [tex]H_o : \mu = 200[/tex]

The Alternative  hypothesis is  

     [tex]H_a : \mu < 200[/tex]

The test statistics is mathematically represented as

       [tex]t_s = \frac{\= x - \mu }{\frac{\sigma}{\sqrt{n} } }[/tex]

substituting values  

     [tex]t_s = \frac{ 205.7 - 200 }{\frac{21}{\sqrt{70} } }[/tex]

     [tex]t_s = 2.270[/tex]

Now the p-value is mathematically represented as

      [tex]p-value = P(Z \le t_s )[/tex]

substituting values  

      [tex]p-value = P(Z \le 2.270 )[/tex]

Using the Excel function[=NORMDIST(2.270)] to calculate the p-value we obtain that

       [tex]p-value = 0.013167[/tex]

Answer:

A) 0.012

From CollegeBoard

Answer:

63%

225 buyers

Step-by-step explanation:

To find the percent take the number that liked it over the total

376/600

Change to decimal form

.62666666

Change to percent by multiplying by 100

62.66666666%

The nearest percent is 63%

37.5 % would but it then multiply by the number of shoppers

37.5 % ( 600)

Change to decimal form

.375 * 600

225

Answer:

-3

Step-by-step explanation:

-3 is the answer

Answer:

-3

Step-by-step explanation:

Answer:

BC = 10, AC= approximately 13.66 OR 5+5 √3

Step-by-step explanation:

Law of Sines

Answer:

[tex]\mathrm{B.}[/tex] All real numbers except x = 2, x = 5

Step-by-step explanation:

If the denominator is equal to 0 then the function would be undefined.

Set the denominator equal to 0.

x² - 7x + 10 = 0

Factor the left side of the equation.

(x - 5)(x - 2) = 0

Set the factors equal to 0.

x - 5 = 0

x = 5

x - 2 = 0

x = 2

The domain is all real numbers except x = 2 and x = 5.

Answer:

x = 1 3/22

Step-by-step explanation:

1/2 x + 3/5 x = 5/4

We need to get rid of the fractions by multiplying by 20 on each side

20 (1/2 x + 3/5 x) = 20 * 5/4

Distribute

10x + 12x = 25

Combine like terms

22x = 25

Divide each side by 22

22x/22 = 25/22

x = 22/22 + 3/22

x = 1 3/22

Answer:

[tex]x = 1\frac{3}{22}[/tex]

Step-by-step explanation:

=> [tex]\frac{1}{2} x + \frac{3}{5} x = \frac{5}{4}[/tex]

LCM = 20

So, Multiplying both sides by 20

=> [tex]20 (\frac{x}{2} + \frac{3x}{5}) = 5 * 5[/tex]

[tex]10 * x + 4*3x = 25\\10x+12x = 25\\22x = 25[/tex]

Dividing both sides by 22

[tex]x = \frac{25}{22}[/tex]

[tex]x = 1\frac{3}{22}[/tex]

Answer:

C (the third table, from the second picture).

Step-by-step explanation:

First, we need to find the slope of the graph.

Two conspicuous points are (0, -3) and (2, 1).

The slope is: (1 - -3) / (2 - 0) = (1 + 3) / 2 = 4 / 2 = 2.

A: In the table, the y-values increase by 2, while the x-values increase by 4. 2 / 4 = 1 / 2 = 0.5. The slope is not the same as the graph.

B: In the table, the y-values decrease by 2, while the x-values increase by 4. -2 / 4 = -1 / 2 = -0.5. The slope is not the same as the graph.

C: In the table, the y-values increase by 4, while the x-values increase by 2. 4 / 2 = 2 / 1 = 2. The slope is the same as the graph, so C is your answer.

D: In the table, the y-values decrease by 4, while the x-values increase by 2. -4 / 2 = -2 / 1 = -2. The slope is not the same as the graph.

Hope this helps!

Answer:

∠CAB ≅ ∠SAB is not true

Step-by-step explanation:

CPCTC means id ABC = XYZ, than A=X, AB=XY, C=Z and so on. Basically the number numbers that come in the same order as the other one is equal.

So ∠CAS ≅ ∠BAS is true but ∠CAB ≅ ∠SAB is not.

Hope this helps. If you have any follow-up questions, feel free to ask.

Have a great day! :)

Answer:

sap

Step-by-step explanation:

Answer:

The graph of g( x ) is the graph of f(x) stretched vertically by a factor of 2.

Option C is the correct option.

Step-by-step explanation:

Solution,

f ( x ) = 2ˣ

g ( x ) = 2 ( 2 ˣ )

2 is multiplied with f(x)

2 is greater than 1

so, Vertical stretch by a factor of 2.

Option C is correct.

Hope this helps...

Best regards!!

We want to compare the functions f(x) and g(x), given that we know that g(x) is a transformation of f(x).

The correct option is B, "the graph of g(x) is the graph of f(x) stretched vertically by a scale factor of 2."

Here we know that:

f(x)  =2^x

g(x) = 2*f(x) = 2*2^x

First, remember that a general vertical dilation/stretch of scale factor k is written as:

g(x) = k*f(x)

So only by that and knowing that g(x) = 2*f(x), we can conclude that the graph of g(x) is the graph of f(x) dilated/stretched vertically by a scale factor of 2.

Then the correct option is B, "the graph of g(x) is the graph of f(x) stretched vertically by a scale factor of 2."

If you want to learn more, you can read:

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Answer:

Step-by-step explanation:

Given that:

the standardized test scores of the students in a school are normally distributed with:

mean = 85 points

standard deviation = 3 points

Using the empirical rule:

=85 - (3 × 3)

= 85 - 9

= 76

The given value of 76 points is 3 standard deviations below mean

Therefore;

the percent score between the given value of 76 points and the  mean 85 points is:

99.7/2 = 49.85%   ( since 99.7 data value lies within 3 standard deviation)

Also ; the percent of value above the mean score = 50%

Therefore, the probability that a student's score is greater than 76 points is

= (49.85 + 50 )%

 = 99.85%

Answer:

mean=85

sd=3

85-3*3=76

its between 76 and 85=99.7/2=49.85%

50% mean above.

49.85+50=99.85%

Step-by-step explanation:

Answer:

Option C - Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in

Step-by-step explanation:

We are given;

n = 15

t-value = 1.66

Significance level;α = 0.05

So, DF = n - 1 = 15 - 1 = 14

From the one-sample t - table attached, we can see that the p - value of 0.06 at a t-value of 1.66 and a DF of 14

Now, since the P-value is 0.06,it is greater than the significance level of 0.05. Thus we do not reject the null hypothesis. We conclude that there is not sufficient evidence that the true diameter differs from 0.5 in.

Answer:

21

Step-by-step explanation:

Just like a dilation you want to find some sort of scale factor. Now when 7/2 is simplified it then becomes 3.5. Now multiply that by 6 since we are trying to find the ratio. when multiplied by 6 it becomes 21 so the ration of wins to losses is 21/6

Answer:  A) -2

Step-by-step explanation:

The y-intercept (where the graph crosses the y-axis) is the "initial value".

Looking at the given graph, it crosses the y-axis when y = -2

Answer:

[tex]\boxed{(-\frac{\sqrt{3}}{2}, \frac{1}{2})}[/tex]

Step-by-step explanation:

Method 1: Using a calculator instead of the unit circle

The unit circle gives coordinates pairs for the cos and sin values at a certain angle. Therefore, if an angle is given, use a calculator to evaluate the functions at cos(angle) and sin(angle).

Method 2: Using the unit circle

Use the unit circle to locate the angle measure of 150° (or 5π/6 radians) and use the coordinate pair listed by the value.

This coordinate pair is (-√3/2, 1/2).

Answer: This coordinate pair is (-√3/2, 1/2).

Step-by-step explanation:

Use the unit circle to locate the angle measure of 150° (or 5π/6 radians) and use the coordinate pair listed by the value.

Step-by-step explanation:

The first six terms for each of the following sequenses are:

(a) a_n = 3n - 10

1. a_1 = -7

2. a_2 = -4

3. a_3 = -1

4. a_4 = 2

5. a_5 = 5

6. a_6 = 8

(b) a_n = (1 + (-1)^n) ^n

1. a_1 = 0

2. a_2 = 4

3. a_3 =0

4. a_4 = 16

5. a_5 = 0

6. a_6 = 32

Answer:

y = 3 |x − 8| + 1

Step-by-step explanation:

y = 3 |x|

Shift right 8 units:

y = 3 |x − 8|

Shift up 1 unit:

y = 3 |x − 8| + 1